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Question
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
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Solution
Let I = `int (sin6x)/(sin 10x sin 4x).dx`
= `int (sin (10x - 4x))/(sin 10x sin 4x).dx`
= `int (sin 10x cos 4x - cos 10x sin 4x)/(sin 10x sin 4x).dx`
= `int [(sin 10x cos 4x)/(sin 10x sin 4x) - (cos 10x sin 4x)/(sin 10x sin 4x)].dx`
= `int cot 4x dx - int cot 10x dx`
= `(1)/(4)log|sin4x| - (1)/(10)log|sin 10x| + c`.
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